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Mathematics  2011 

Some results on the generic vanishing of Koszul cohomology via deformation theory

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Abstract:

We study the deformation-obstruction theory of Koszul cohomology groups of $g^r_d$'s on singular nodal curves. We compute the obstruction classes for Koszul cohomology classes on singular curves to deform to a smooth one. In the case the obstructions are nontrivial, we obtain some partial results for generic vanishing of Koszul cohomology groups.

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